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Chapter 31: Problem 42

At what two distances could you place an object from a \(45-\mathrm{cm}-\) focal-length concave mirror to get an image 1.5 times the object's size?

Short Answer

Expert verified
The two distances at which you could place the object are approximately -22.5 cm and -90.0 cm from the concave mirror.

Step by step solution

01

Apply the magnification formula

We can start by rearranging the magnification formula to solve for the image distance (v). The magnification (m) is equal to -v/u, so we can express v in terms of m and u: v = -mu
02

Substitute in the lens formula

The lens formula is 1/f = 1/v + 1/u. We'll substitute v from Step 1 into this formula and solve the equation for u.
03

Solve the resulting quadratic equation

Solving for u will result in a quadratic equation, which can be factored or solved using the quadratic formula. The two solutions correspond to the two different situations in which the image is 1.5 times the size of the object.
04

Find both values of u

The two solutions represent the two possible distances at which the object could be placed. It's important to note that the sign conventions used in physics mean that a negative distance implies the object is on the same side of the mirror as the light being reflected, while a positive distance implies the object is on the opposite side of the mirror from the light being reflected.

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Most popular questions from this chapter

Show that identical objects placed equal distances on either side of the focal point of a concave mirror or converging lens produce images of equal size. Are the images of the same type?

A double-convex lens with equal 28.5 -cm curvature radii is made from glass with refractive indices \(n_{\mathrm{red}}=1.512\) and \(n_{\text {violet }}=1.547 .\) If a point source of white light is located on the lens axis at \(75.0 \mathrm{cm}\) from the lens, over what distance will its visible image be smeared?

A candle is on the axis of a \(15-\mathrm{cm}\) -focal-length concave mirror, \(36 \mathrm{cm}\) from the mirror. (a) Where is its image? (b) How do the image and object sizes compare? (c) Is the image real or virtual?

(a) Find the focal length of a concave mirror if an object placed \(38.4 \mathrm{cm}\) in front of the mirror has a real image \(55.7 \mathrm{cm}\) from the mirror. (b) Where and what type will the image be if the object is moved to a point \(16.0 \mathrm{cm}\) from the mirror?

An object is \(68 \mathrm{cm}\) from a plano-convex lens whose curved side has curvature radius \(26 \mathrm{cm} .\) The refractive index of the lens is 1.62. Where is the image, and what type is it?
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